Introduction

Land-mobile communication is burdened with particular
propagation complications compared to the channel characteristics in radio
systems with fixed and carefully positioned antennas. The antenna height
at a mobile terminal is usually very small, typically less than a few meters.
Hence, the antenna is expected to have very little 'clearance', so obstacles
and reflecting surfaces in the vicinity of the antenna have a substantial
influence on the characteristics of the propagation path. Moreover, the
propagation characteristics change from place to place and, if the mobile
unit moves, from time to time. Thus, the transmission path between the
transmitter and the receiver can vary from simple direct line of sight
to one that is severly obstructed by buildings, foliage and the terrain.

In generic system studies, the mobile radio channel is usually evaluated
from 'statistical' propagation models: no specific terrain data is considered,
and channel parameters are modelled as stochastic variables. The mean signal
strength for an arbitrary transmitter-receiver (T-R) separation is useful
in estimating the radio coverage of a given transmitter whereas measures
of signal variability are key determinants in system design issues such
as antenna diversity and signal coding.

Multipath propagation leads to rapid fluctuations
of the phase and amplitude of the signal if the vehicle moves over a distance
in the order of a wave length or more. Multipath fading thus has a 'small-scale'
effect.

Shadowing is a 'medium-scale' effect: field
strength variations occur if the antenna is displaced over distances larger
than a few tens or hundreds of metres.

The 'large-scale' effects of path losses cause
the received power to vary gradually due to signal attenuation determined
by the geometry of the path profile in its entirety. This is in contrast
to the local propagation mechanisms, which are determined by builfing and
terrain features in the immediate vicinity of the antennas.

The large-scale effects determine a power level
averaged over an area of tens or hundreds of metres and therefore called
the 'area-mean' power. Shadowing introduces additional
fluctuations, so the received local-mean power varies around the area-mean.
The term 'local-mean' is used to denote the signal level averaged over
a few tens of wave lengths, typically 40 wavelengths. This ensures that
the rapid fluctuations of the instantaneous received power due to multipath
effects are largely removed.

Path Loss: Models of "large-scale effects"

Example

The most appropriate path loss model depends on the location of the receiving
antenna. For the example above at:

Path-loss law

Free Space Propagation

For propagation distances d much larger than the square of the
antenna size divided by the wavelength, the far-field of the generated
electromagnetic wave dominates all other components (in the far-field region
the electric and magnetic fields vary inversely with distance). In free
space, the power radiated by an isotropic antenna is spread
uniformly and without loss over the surface of a sphere surrounding the
antenna. An isotropic antenna is a hypothetical entity!! Even the simplest
antenna has some directivity. For example, a linear dipole has uniform
power flow in any plane perpendicular to the axis of the dipole (omnidirectionality)
and the maximum power flow is in the equatorial plane (see Appendix 1:
Antenna Fundamentals).

The surface area of a sphere of radius d is 4d2,
so that the power flow per unit area w(power flux in watts/meter2)
at distance d from a transmitter antenna with input accepted power
pTand antenna gain GTis

.

Transmitting antenna gain is defined as the ratio of the intensity
(or power flux) radiated in some particular direction to the radiation
intensity that would be obtained if the power accepted by the antenna were
radiated isotropically. When the direction is not stated, the power gain
is usually taken in the direction of maximum power flow. The product GT
pT is called the effective radiated power
(ERP) of the transmitter. The available power pR
at the terminals of a receiving antenna with gain GR
is

where A is the effective area or aperture of
the antenna and
(see Appendix 1: Antenna Fundamentals).
The wavelength =
c / fc with c the velocity of light and fcthe
carrier frequency.

While cellular telephone operator mostly calculate in received powers,
in the planning of the coverage area of broadcast transmitters, the CCIR
recommends the use of the electric field strength E at the location
of the receiver. The conversion is .

Exercise:

Show that for a reference transmitter with ERP of 1 kwatt in free space,

As the propagation distance increases, the radiated energy is spread
over the surface of a sphere of radius d, so the power received
decreases proportional to d2. Expressed in dB, the received
power is

Exercise:

Show that the path loss L between two isotropic antennas (GR
= 1, GT = 1) can be expressed as

L (dB)= - 32.44 - 20 log ( fc/ 1MHz)
- 20 log (d / 1km)

which leads engineers to speak of a "20 log d" law.

Propagation over a Plane Earth

If we consider the effect of the earth surface, the expressions for
the received signal become more complicated than in case of free
space propagation. The main effect is that signals reflected off the
earth surface may (partially) cancel the line of sight wave.

Model

For an isotropic or omnidirectional antenna
above a plane earth, the received electric field strength is

with Rgthe reflection coefficient and E0
the field strength for propagation in free space. This expression can be
interpreted as the complex sum of a direct line-of-sight wave, a ground-reflected
wave and a surface wave. The phasor sum of the first and second term is
known as the space wave.

For a horizontally-polarized wave incident on the surface of a perfectly
smooth earth,

whereris
the relative dielectric constant of the earth,
is the angle of incidence (between the radio ray and the earth surface)
and x = /(2
fc0)
with the
conductivity of the ground and 0
the dielectric constant of vacuum.

For vertical polarization

Exercise

Show that the reflection coefficient tends to -1 for angles close to
0. Verify that for vertical polarization, abs( Rc) >
0.9 for <10 degrees. For horizontal
polarization, abs( Rc) > 0.5 for
< 5 degrees and abs( Rc) > 0.9 for
< 1 degree.

UHF Mobile Communication

The relative amplitude F(.) of the surface wave is very small
for most cases of mobile UHF communication (F(.) << 1). Its
contribution is relevant only a few wavelengths above the ground. The phase
difference between the direct and the ground-reflected wave can be found
from the two-ray approximation considering only a Line-of-Sight and a Ground
Reflection. Denoting the transmit and receive antenna heights as hT
and hR, respectively, the phase difference can be expressed
as

For large d, one finds, using the
expression

,

For large d, (d >> 5hT hR ),
the reflection coefficient tends to -1, so the received signal power
becomes

For propagation distances substantially beyond the turnover point --
i.e. --
this expression tends to the fourth power distance law:

Exercise

Discuss the effect of path loss on the performance
of a cellular radio network. Is it good to have signals attenuate rapidly
with increasing distance?

Egli's Model (1957)

Experiments confirm that in macro-cellular links over smooth, plane
terrain, the received signal power (expressed in dB) decreases with "40
log d". Also a "6 dB/octave" height gain is experienced:
doubling the height increases the received power by a factor 4.

In contrast to the theoretical plane earth loss, Egli measured a significant
increase of the path loss with the carrier frequency fc.
He proposed the semi-empirical model

For communication at short range, this formula looses its accuracy because
the reflection coefficient is not necessarily close to -1. For ,
free space propagation is more appropriate, but a number
of significant reflections must be taken into account. In streets with
high buildings, guided propagation may occur.

Diffraction loss

If the direct line-of-sight is obstructed by a single object ( of height
hm), such as a mountain or building, the attenuation
caused by diffraction over such an object can be estimated by treating
the obstruction as a diffracting knife-edge.

Figure: Path profile model for (single) knife edge diffraction

This is the simplest of diffraction models, and the diffraction loss
in this case can be readily estimated using the classical Fresnel solution
for the field in the shadow behind a half-plane. Thus, the field strength
in the shadowed region is given by

where E0 is the free space field strength
in the absence of the knife-edge and F(v) is the complex Fresnel
integral which is a tabulated function of the diffraction parameter

where dT and dRare the terminal
distances from the knife edge. The diffraction loss, additional to free
space loss and expressed in dB, can be closely approximated by

The attenuation over rounded obstacles is usually higher than Adiff
in the above formula.

Approximate techniques to compute the diffraction loss over multiple
knife edges have been proposed by

Deygout suggested that entire path be searched for a main obstacle,
i.e., the point with the highest value of v along the path.
Diffraction losses over "secondary" obstacles may be added to
the diffraction loss over the main obstacle.

Total Path loss

The previously presented methods for ground reflection
loss and diffraction losses suggest a "Mondriaan"
interpretation of the path profile: Obstacles occur as straight vertical
lines while horizontal planes cause reflections. That is the propagation
path is seen as a collection of horizontal and vertical elements. Accurate
computation of the path loss over non-line-of-sight paths with ground reflections
is a complicated task and does not allow such simplifications.

Many measurements of propagation losses for paths with combined diffraction
and ground reflection losses indicate that knife edge type of obstacles
significantly reduce ground wave losses. Blomquist suggested three methods
that may be used to find the total loss -- viz.

Bullington

Blomquist

Blomquist empirical formula

where Afs is the free space loss,
AR is the ground reflection loss
and Adiff is the multiple knife-edge
diffraction loss in dB values.

Statistical Path Loss Law:

Most generic system studies address networks in which all mobile units
have the same gain, height and transmitter power. For ease of notation,
received signal powers and propagation distances can be normalized. In
macro-cellular networks
(1 km < d < 50 km), the area-mean
received power can be written as

with r the normalized distance and the
path loss exponent. Theoretical values
are, respectively 2 and 4 for free space and plane,
smooth, perfectly conducting terrain. Typical values for irregular
terrain are between 3.0 and 3.4 and in forestal terrain propagation can
be appropriately described as in free space plus some diffraction losses,
but without significant groundwave losses ().
If the propagation model has to cover a wide range of distances, may
vary as different propagation mechanisms dominate at different ranges.
In micro-cellular nets, typically
changes from approximately 2 to approximately 4 at some turnover distance
dg. Experimental values of dg
are between 90 and 300 m for hT between 5 and 20 m and
hR approximately 2m where hT and
hR are, respectively, the heights of the transmitting
and receiving and antennas. These values are in reasonable agreement with
the theoretical expression where is
the wavelength of the transmitted wave.

Many models have been proposed and are used in system design:

Harley suggested a smooth transition model, with

where r is a normalized distance, rg is the
normalized turnover distance, and
is the local-mean power (i.e., the received
power averaged over a few meters to remove to effect of multipath fades).
Studies indicate that actual turnover distances are on the order of 800
meters around 2 GHz. This model neglects the wave-interference pattern
that may be experienced at ranges shorter than rg.

Other models, such as a step-wise transition from "20 log d"
to "40 log d" at the turnover distance, have been proposed. Empirical
values for the path loss exponents and their intervals of validity have
been reported in many papers. See the following table.

Model

Area

1

2

FSL

free space

2

0

Egli

average terrain

0

4

two-ray

plane earth

2

2

Green

London

1.7 to 2.1

2 to 7

Harley

Melbourne

1.5 to 2.5

-0.3 to 0.5

Pickhlotz, et al.

Orlando, Florida

1.3

3.5

Typical Harley Parameters

Multipath in Micro-Cells

The micro-cellular propagation channel typically is Rician
: it contains a dominant direct component, with an amplitude determined
by path loss, a set of early reflected waves adding (possibly distructively)
with the dominant wave, and intersymbol interference caused by the excessively
delayed waves, adding incoherently with the dominant wave.

Shadowing

Experiments reported by Egli in 1957 showed that, for paths longer than
a few hundred meters, the received (local-mean)
power fluctuates with a 'log-normal' distribution about the area-
mean power. "Log-normal" means that the local-mean power
expressed in logarithmic values -- i.e.,

-- has a normal -- i.e., Gaussian distribution. The probability
density function (pdf) of the local-mean power is thus of the form

wheresis the logarithmic standard deviation of the shadowing, expressed in
natural units.

Depth of Shadowing

For average terrain, Egli reported a logarithmic standard deviation
of about 8.3 dB and 12 dB for VHF and UHF frequencies, respectively. Such
large fluctuations are caused not only by local shadow attenuation by obstacles
in the vicinity of the antenna, but also by large-scale effects leading
to a coarse estimate of the area-mean power.

This log-normal fluctuation was called large-area shadowing by
Marsan, Hess and Gilbert; over semi-circular routes in Chicago, with fixed
distance to the base station, it was found to range from 6.5 dB to 10.5
dB, with a median of 9.3 dB. Large-area shadowing thus reflects shadow
fluctuations if the vehicle moves over many kilometres.

In contrast to this, in most papers on mobile propagation, only small-area
shadowing is considered: log-normal fluctuations of the local-mean
power over a distance of tens or hundreds of metres are measured. Marsan
et al. reported a median of 3.7 dB for small area shadowing. Preller and
Koch measured local-mean powers at 10 m intervals and studied shadowing
over 500 m intervals. The maximum standard deviation experienced was about
7 dB, but 50% of all experiments showed shadowing of less than 4 dB.

Implications for Cell Planning

If one extends the distinction between large-area and small-area shadowing,
the definition of shadowing covers any statistical fluctuation of the received
local-mean power about a certain area-mean power, with the latter determined
by (predictable) large-scale mechanisms. Multipath
propagation is separated from shadow fluctuations by considering the local-mean
powers. That is, the standard deviation of the shadowing will depend on
the geographical resolution of the estimate of the area-mean power. A propagation
model which ignores specific terrain data produces about 12 dB of shadowing.
On the other hand, prediction methods using topographical data bases with
unlimited resolution can, at least in theory, achieve a standard deviation
of 0 dB. Thus, the standard deviation is a measure of the impreciseness
of the terrain description. If, for generic system studies, the (large-scale)
path loss is taken of simple form depending only
on distance but not on details of the path profile, the standard deviation
will necessarily be large. On the other hand, for the planning of a practical
network in a certain (known) environment, the accuracy of the large-scale
propagation model may be refined. This may allow a spectrally more efficient
planning if the cellular layout is optimised for the propagation environment.

Combined model by Mawira (Netherlands' PTT Research)

Multiple log-normal signals

In cellular networks, interference does not come from only one source
but from many co-channel transmitters. In a hexagonal reuse pattern the
number of interferers typically is six.

At least two different methods are used to estimate the probability
distribution of the joint interference power accumulated from several log-normal
signals. Such methods are relevant to estimate the joint effect of multiple
interfering signals with shadowing.
Fenton and Schwartz and Yeh both proposed to approximate the pdf of the
joint interference power by a log-normal pdf, yet neither could determine
it exactly.

Fenton

The method by Fenton assesses the logarithmic mean and variance of the
joint interference signal directly as a function of the logarithmic means
and variances of the individual interference signals. This method is most
accurate for small standard deviations of the shadowing, say, for less
than 4 dB.

Schwartz and Yeh

The technique proposed by Schwartz and Yeh is more accurate in the range
of 4 to 12 dB shadowing, which corresponds to the case of land-mobile radio
in the VHF and UHF bands. Their method first assesses the logarithmic mean
and variance of a joint signal produced by cumulation of two signals. Recurrence
is then used in the event of more than two interfering signals. A disadvantage
of the latter method is that numerical computations become time consuming.

Table Mean mt and standard deviation st (both in dB)
of the joint power of n signals with uncorrelated shadowing, each
with mean 0 dB and with identical standard deviation. Networks, with 0,
6, 8.3 and 12 dB of shadowing of individual signals.

Besides these methods, by Fenton and Schwartz and Yeh, a number of alternative
(and often more simplified) techniques are used. For instance in VHF radio
broadcasting, signals fluctuate with location and with time according to
log-normal distributions. Techniques to compute the coverage of broadcast
transmitters are in CCIR recommendations.

Outage probabilities for systems with multiple Rayleigh
fading and shadowed signals can however be computed easily without explicitly
estimating the joint effect of multiple shadowed signals.

Multipath Reception

The mobile or indoor radio channel is characterized by 'multipath reception':
The signal offered to the receiver contains not only a direct line-of-
sight radio wave, but also a large number of reflected radio waves.

These reflected waves interfere with the direct wave, which causes significant
degradation of the performance of the network. A wireless network has to
be designed in such way that the adverse effect of these reflections is
minimized.

Although channel fading is experienced as an unpredictable, stochastic
phenomenon, powerful models have been developed that can accurately predict
system performance.

Most conventional modulation techniques are sensitive to intersymbol
interference unless the channel symbol rate is small compared to the delay
spread of the channel. Nonetheless, a signal received at a frequency
and location where reflected waves cancel each other, is heavily attenuated
and may thus suffer large bit error rates.

Models for multipath reception

Narrowband Rayleigh, or Rician
models mostly address the channel behaviour at one frequency only. Dispersion
is modelled by the delay spread.

The effect of multipath reception

for a fast moving user: rapid fluctuations of the
signal amplitude and phase

for a wideband (digital) signal: dispersion
and intersymbol interference

for an analog television signal: "ghost" images (shifted
slightly to the right)

for a multicarrier signal: different attenuation at different (sub-)carriers
and at different locations

for a stationary user of a narrowband system: good reception at some
locations and frequencies; poor reception at other locations and frequencies

for a satellite positioning system: strong delayed reflections may
cause a severe miscalculation of the distance between user and satellite.
This can result in a wrong "fix"

Rician fading

The model behind Rician fading is similar to that for Rayleigh
fading, except that in Rician fading a strong dominant component is
present. This dominant component can for instance be the line-of-sight
wave. Refined Rician models also consider

that the dominant wave can be a phasor sum of two or more dominant
signals, e.g. the line-of-sight, plus a ground
reflection. This combined signal is then mostly treated as a deterministic
(fully predictable) process.

that the dominant wave can also be subject to shadow
attenuation. This is a popular assumption in the modelling of satellite
channels.

Besides the dominant component, the mobile antenna receives a large
number of reflected and scattered waves.

PDF of signal amplitude

The derivation is similar to the derivation
for Rayleigh fading. In order to obtain the probability density of
the signal amplitude we observe
the random processes I(t) and Q(t) at one particular instant
t0. If the number of scattered waves is sufficiently
large, and are i.i.d., the central limit theorem says that I(t0)
and Q(t0) are Gaussian, but, due to the deterministic
dominant term, no longer zero mean. Transformation of variables shows that
the amplitude and the phase have the joint pdf

Here, is the local-mean
scattered power and C2/2 is the power of the dominant component.
The pdf of the amplitude is found from the integral

,

where I0(..) is the modified Bessel function of the first
kind and zero order, defined as

Exercise:

Show that the total local-mean power is

Rician factor

The Rician K-factor is defined as the ratio of signal power in
dominant component over the (local-mean) scattered power. Thus

Expressed in terms of the local-mean power
and the Rician K-factor, the pdf of the signal amplitude becomes

Exercise

Show that for a large local-mean signal-to-noise ratio
, the probability that the instantaneous power p drops below a noise
threshold tends
to

Rician Channels

Examples of Rician fading are found in

Microcellular channels

Vehicle to Vehicle communication, e.g., for AVCS

Indoor propagation

Satellite channels

Rayleigh fading

Rayleigh fading is caused by multipath reception.
The mobile antenna receives a large number, say N, reflected and
scattered waves. Because of wave cancellation effects, the instantaneous
received power seen by a moving antennna becomes a random variable, dependent
on the location of the antenna.

In case of an unmodulated carrier, the transmitted signal has the form

.

Next we'll discuss the basic mechanisms of mobile reception.

Effect of Motion

Let the n-th reflected wave with amplitude cn
and phase arrive
from an angle
relative to the direction of the motion of the antenna.

If the set of reflected waves are dominated by one strong component,
Rician fading is a more appropriate
model.

Doppler spectrum

Doppler shifts

We consider a Rayleigh fading signal. Let the
n-th reflected wave with amplitude cn and phase
arrive from an
angle relative
to the direction of the motion of the antenna.

The Doppler shift of this wave is

where v is the speed of the antenna.

Such motion of the antenna leads to phase shifts of individual reflected
waves, so it affects the amplitude of the resulting
signal. It is often assumed that the angle is uniformly distributed within
[0, 2 ]. This allows us to compute a
probability density function of the frequency of incoming waves. Assuming
that the number of waves is very large, we can obtain the Doppler spectrum
of the received signal.

Let the n-th reflected wave with amplitude cn
and phase arrive
from an angle
relative to the direction of the motion of the antenna.

If the mobile antenna moves a small distance d,
the n-th incident wave, arriving from the angle
with respect to the instantaneous direction of motion, experiences a phase
shift of

(2d/) cos( )

Thus all waves experience their own phase rotation. The resulting vector
may significantly change in amplitude if individual components undergo
different phase shifts.

Figure: Phasor diagram of a set of scattered waves after
antenna displacement (in blue)
and before motion (in light blue), resulting a Rayleigh-fading envelope
(in black)

In mobile radio channels with high terminal speeds, such changes occur
rapidly. Rayleigh fading then causes the signal amplitude and phase to
fluctuate rapidly.

If d is in the order of half a wave length (/2)
or more, the phases of all incident waves become mutually uncorrelated,
thus also the amplitude of the total received signal becomes uncorrelated
with the amplitude at the point of departure.

Doppler Shifts

Each reflected wave experiences its own Doppler shift.
If an unmodulated carrier is being transmitted, a spectrum of different
components is received.

Autocovariance

The normalised covariance L(d) of the electric field strength
for an antenna displacement d is of the form

with J0(.) the zero-order Bessel function of the first
kind.
The signal remains almost entirely correlated for a small displacement,
say d< /8,
but becomes rapidly independent for larger displacements, say for d>
/2.

Figure: Auto-covariance L(d) of the electric field
strength in a Rayleigh-fading channel
versus the normalised antenna displacement d/
in horizontal direction.

The antenna displacement can also be expressed
in the terminal velocity v and the time difference T between
the two samples (d = v T). So with fm the maximum
Doppler shift (fm = v fc / c).

Analog Transmission over Fading Channels

Amplitude modulation

Various methods exist to transmit a baseband message m(t) using
an RF carrier signal c(t) = Ac cos ( c
t + ). In linear modulation,
such as Amplitude Modulation (AM) and Single Side band (SSB) the amplitude
Ac is made a linear function of the message m(t).

Figure: Phasor Diagram for AM with tonal modulation.

AM has the advantage that the detector circuit can be very simple. This
allows inexpensive production of mediumwave broadcast receivers. The transmit
power amplifier, however, needs to be highly linear and therefor expensive
and power consuming.

For mobile reception of AM audio signals above 100 MHz, the spectrum
of channel fluctuations due to fading
and in the message overlap. Hence the Automatic Gain Control in the receiver
IF stages can not distinguish the message and channel fading. AGC will
thus distort the message m(t).

AM is only rarely used for mobile communication, although it is still
used for radio broadcasting.

Single Side Band

In the frequency power spectrum of AM signals we recognize an upper
side band and a lower side sideband, with frequency components above and
below the carrier at fc. In Single Side Band transmission,
the carrier and one of these side bands are removed.

An SSB message can be recovered by multiplying the received signal by
cos(ct +
). If the local oscillator has a phase offset (
- ), the detected signal is a linear
combination of the orginal message m(t) and a 90 degree phase-shifted
version (its Hilbert transform). The human ear is not very sensitive to
such phase distortion; therefor the detected signal sounds almost identical
to m(t), despite any phase offset. However, such phase shifts make
SSB unsuitable for digital transmission.

The effect of a frequency error in the local oscillator is more dramatic
to analog speech signals. Its effect can best be understood from the frequency
domain description of the SSB signal. A frequency shift of all baseband
tones occurs. In this case, the harmonic relation between audio tones is
lost and the signal sounds very artificial.

SSB is relatively sensitive to interference, which requires large frequency
reuse spacings and severely limits the spatial spectrum efficiency of cellular
SSB networks.

AGC to reduce the effect of amplitude fades substantially affects the
message signal. Furthermore, SSB requires very sharp filters, which are
mostly sensitive to physical damage, temperature and humidity changes.
This makes SSB not very attractive for mobile communication.

PHASE MODULATION

In phase modulation, the transmit signal has the constant-amplitude
form

After frequency-nonselective multipath propagation, a received FM signal

contains random phase and frequency modulation, which are additive
to the modulation

suffers from dispersion. The audio signal will be distorted.

Reception above the FM-Threshold

If the signal-to-noise ratio is sufficiently large, the received signal
is dominated by the wanted signal. The effect of noise can be approximated
as a liniear additive distrurbance. The minimum signal-to-noise ratio for
which this assumption is reasonable is called the FM capture threshold.

Capture

In non-linear modulation, such as phase modulation (PM) or frequency
modulation (FM), the post-detection signal-to-noise ratio can be greatly
enhanced as compared to baseband transmission or compared to linear modulation.
This enhancement occurs as long as the received pre-detection signal-to-noise
ratio is above the threshold. Below the threshold the signal-to-noise ratio
deteriorates rapidly. This is often perceived if the signal-to-noise ratio
(C/N) increases slowly: a sudden transition from poor to good reception
occurs. The signal appears to "capture" the receiver at certain
C/N. A typical threshold value is 10 (10 dB) C/N at RF. The audio SNR where
capture occurs depends on the frequency deviation.

Effects of Rayleigh fading on FM reception

In a rapidly fading channel, the events of crossing the FM capture threshold
may occur too frequently to be distinguished as individual drop outs. The
performance degradation is perceived as an average degradation of the channel.
The capture effect and the FM threshold vanish in such situations.

Effect of Amplitude variations

Fluctuations of the signal-to-noise ratio cause fluctuations of received
noise power and fluctuations of the amplitude of the detected wanted signal.
Some analyses assume that the difference between the detected signal and
the expected signal is perceived as a noise type of disturbance. It is
called the signal-suppression 'noise', even though disturbances that are
highly correlated with the signal are mostly perceived as 'distortion'
rather than as noise.

Effect of Random FM

For large local-mean signal-to-noise ratios Random FM is the only remaining
factor. For voice communication with audio passband 300 - 3000 Hz, the
noise contribution due to random FM leads to a SNR of

with S the audio power at the detector output. This does not
depend on additive predection noise. Wideband transmission (large frequency
deviation) is thus significantly less sensitive to random FM than narrowband
FM.

Threshold Crossing Rate

The average number of times per second that a fading signal crosses
a certain threshold is called the threshold crossing rate. Lets enlarge
the following (orange) signal path, at the (yellow) instant when it crosses
the (purple) threshold.

The above crossing of the threshold R with width dr lasts
for dt seconds. The derivative of the signal amplitude, with respect
to time, is dr / dt.

If the signal always crosses the threshold with the same derivative,
then:

Average number of crossings per second * dt = Probability
that the amplitude is in the interval [R, R + dr].

The probability that the signal amplitude is within the window [R,
R + dr] is known from the probability density of the signal amplitude,
which can for instance be Rayleigh,
Rician or Nakagami.
Moreover, the joint pdf of signal amplitude and its derivative can be found.
For a Rayleigh-fading signal.

The TCR curve has a maximum if the local-mean-power is about as large
as the threshold noise or interference power. If the signal is on average
much stronger than the threshold, the number of threshold crossings (i.e.,
deep fades) is relatively small. Also, if the signal is much weaker than
the threshold, the number of crossings is small because signal "up-fades"
are unlikely.

Fade Duration

The mobile Rayleigh or Rician
radio channel is characterized by rapidly changing channel
characteristics. If a certain minimum (threshold) signal level is needed
for acceptable communication performance, the received signal will experience
periods of

sufficient signal strength or "non-fade intervals"

insufficient signal strength or "fades"

It is of critical importance to the performance of mobile data networks
that the used packet duration is selected taking into account the expected
duration of fades and non-fade intervals.

The curve for n = 6 closely resembles the curve the ANFD in an
interference-free but noise-limited channel.

Thus

The ANFD is proportional to the speed of the mobile user. Channel fading
occurs mainly because the user moves. If the user is stationary almost
no time variations of the channel occur (except if reflecting elements
in the environment move).

The ANFD increases proportional with the square root of the fade margin.

The non-fade duration is not so sensitive to whether the signal experiences
fades below a constant noise-floor or a fading interfering signal.

Calculation of the distribution of non-fade periods is tedious, but
has been elaborated by Rice. Because of the shape of the Doppler spectrum,
fade durations that coincide with a motion of about half a wavelength are
relatively frequent.

The average fade duration (AFD) is

Thus

The AFD is proportional to the speed of the mobile user.

The fade durations rapidly reduce with increasing fade margin, but
the time between fades increases much slower.

Experiments revealed that at large fade margins, the fade durations
are approximately exponentially distributed around their mean value.

Delay Spread

Because of multipath reflections, the channel
impulse response of a wireless channel looks likes a series of pulses.

Figure: Example of impulse response and frequency transfer
function of a multipath channel.

We can define the local-mean average received
power with excess delay within the interval (T, T + dt).
This gives the "delay profile" of the channel.

The delay profile determines to what extent the channel fading at two
different frequencies f1 and f2 are
correlated.

Some definitions

The maximum delay time spread is the total time interval during which
reflections with significant energy arrive.

The rms delay spread Trms is the standard deviation
(or root-mean-square) value of the delay of reflections, weighted proportional
to the energy in the reflected waves.

For a digital signal with high bit rate, this dispersion is experienced
as frequency selective fading and intersymbol interference (ISI). No serious
ISI is likely to occur if the symbol duration is longer than, say, ten
times the rms delay spread.

Typical Values

In macro-cellular mobile radio, delay spreads are mostly in the range
from Trms is about 100 nsec to 10 microsec. A typical
delay spread of 0.25 microsec corresponds to a coherence
bandwidth of about 640 kHz. Measurements made in the U.S., indicated
that delay spreads are usually less than 0.2 microsec in open areas, about
0.5 microsec in suburban areas, and about 3 micros in urban areas. Measurements
in The Netherlands showed that delay spreads are relatively large in European-style
suburban areas, but rarely exceed 2 microsec. However, large distant buildings
such as apartment flats occasionally cause reflections with excess delays
in the order of 25 microsec.

In indoor and micro-cellular channels, the delay
spread is usually smaller, and rarely exceed a few hundred nanoseconds.
Seidel and Rappaport reported delay spreads in four European cities of
less than 8 microsec in macro-cellular channels, less than 2 microsec in
micro-cellular channels, and between 50 and 300 ns in pico-cellular channels.

Resolvable Paths

A wideband signal with symbol duration Tc (or a direct
sequence (DS)-CDMA signal with chip time Tc), can "resolve"
the time dispersion of the channel with an accuracy of about Tc.
For DS-CDMA, the number of resolvable paths is

N = round (Tdelay / Tchip ) +
1

where round(x) is the largest integer value smaller
than x and Tdelay is total length of the delay
profile. A DS-CDMA Rake receiver
can exploit N- fold path diversity.

Coherence Bandwidth

One can define 'narrowband' transmission defined in the time domain,
considering interarrival times of multipath reflections
and the time scale of variations in the signal caused by modulation. A
signal sees a narrowband channel if the bit duration is sufficiently larger
than the interarrival time of reflected waves. In such case, the intersymbol
interference is small.

Transformed into constraints in the frequency domain, this criterion
is found to be satisfied if the transmission bandwidth does not substantially
exceed the 'coherence' bandwidth Bc of the channel. This
is the bandwidth over which the channel transfer function remains virtually
constant.

For a Rayleigh-fading channel with an exponential
delay profile, one finds

Scatter Function

The scatter function combines information about Doppler
shifts and path delays. Each path can be described
by its

Angle of arrival and Doppler shift

Excess delay

Thus we can plot the received energy in a two dimensional plane, with
Doppler shift on one horizontal axis and delay on the other horizontal
axis.

Reciprocity - differences between uplink and
downlink

Two-way communication requires facilities for 'inbound', i.e., mobile-to-fixed,
as well as 'outbound', i.e., fixed-to-mobile communication. In circuit-switched
mobile communication, such as cellular telephony, the inbound and outbound
channel are also called the 'uplink' and 'downlink', respectively. The
propagation aspects described on other pages are
valid for inbound and outbound channels. This is understood from the reciprocity
theorem:

If, in a radio communication link, the role of the receive and transmit
antenna are functionally interchanged, the instantaneous transfer characteristics
of the radio channel remain unchanged.

In mobile multi-user networks with fading channels,
the reciprocity theorem does not imply that the inbound channel behaves
identically as the outbound channel. Particular differences occur for a
number of link aspects:

man-made noise levels
The antenna of the base station is usually mounted on an appropriate antenna
mast, such that it does not suffer from attenuation caused by obstacles
in its vicinity. The mobile antenna, on the other hand, is at most mounted
a few metres above ground level. The man-made noise level, particularly
automotive ignition noise, is likely to be substantially higher at the
mobile antenna than at the base station antenna.

effect of antenna diversity Multipath scatters mostly occur in the immediate
vicinity of the mobile antenna. The base station receives more or less
a transversal electromagnetic wave, whereas the mobile station receives
a superposition of a set of reflected waves from random angles. Two antennas
at the mobile terminal are likely to receive uncorrelated
signal powers if their separation is more than a wave length. At the
base station site, however, all reflections arrive from almost identical
directions. Therefore, diversity at the base station requires much larger
separation of the antennae to ensure uncorrelated received signal powers
at the two antennas. For the same reason, antenna directivity has different
effects at the mobile and the base station.

correlation of shadow fading of wanted signal and interfering signals
In a cellular network, shadow fading of the wanted
signal received by the mobile station is likely to be correlated with the
shadow fading of the interference caused by other base stations, or, in
a spread-spectrum network, with the shadowing of simultaneously transmitted
signals from the same base station. In contrast to this, at the base station,
shadow fading of the wanted signal presumably is mostly statistically independent
from shadow fading of the interference. However, experimental results for
correlation of shadow attenuation are scarce.

full-duplex channels In full-duplex operation, multipath fading of
inbound and outbound channel, which operate at widely different frequencies,
may be uncorrelated. This will particularly be the case if the delay spread
is large.

multiplexing and multiple access
In a practical multi-user system with intermittent transmissions, inbound
messages are sent via a multiple-access channel, whereas in outbound channel,
signals destined for different users can be multiplexed. In the latter
case, the receiver in a mobile station can maintain carrier and bit synchronisation
to the continuous incoming bit stream from the base station, whereas the
receiver in the base station has to acquire synchronisation for each user
slot. Moreover, in packet-switched data networks, the inbound channel has
to accept randomly occurring transmissions by the terminals in the service
area. Random-access protocols are required to organise the data traffic
flow in the inbound channel, and access conflicts ('contention') may occur.

In cellular networks with large traffic loads per base station, spread-spectrum
modulation can be exploited in the downlink to combat multipath fading,
whereas in the uplink, the signal powers from the various mobile subscribers
may differ too much to effectively apply spread- spectrum multiple access
unless sophisticated adaptive power control techniques are employed.

industrial design
From a practical point of view, the downlink and the uplink will be designed
under entirely different (cost) constraints, such as power consumption,
size, weight and other ergonomic aspects, energy radiated into the human
body, and consumer cost aspects.

data traffic patterns
In packet data networks applied for traffic and transportation, the characteristics
of the data traffic flows are known to differ for the uplink and the downlink.
For instance, (outbound) messages from a fleet management centre to the
vehicles are likely to be of a more routine type, of a more uniform length
and occur in a more regular pattern than messages in the opposite (inbound)
direction.

Indoor Wireless RF Channel

There are several causes of signal corruption in an indoor wireless
channel. The primary causes are signal attenuation due to distance,
penetration losses through walls and floors and multipath
propagation.

Effect of distance

Signal attenuation over distance is observed when the mean received
signal power is attenuated as a function of the distance from the transmitter.
The most common form of this is often called free
space loss and is due to the signal power being spread out over the
surface area of an increasing sphere as the receiver moves farther from
the transmitter.

In addition to free space loss effects, the signal experiences decay
due to ground wave loss although this typically only
comes into play for very large distances (on the order of kilometers).
For indoor propagation this mechanism is less relevant, but effects of
wave guidance through corridors can occur.

Multipath

Multipath results from the fact that the propagation channel consists
of several obstacles and reflectors. Thus, the received signal arrives
as an unpredictable set of reflections and/or direct waves each with its
own degree of attenuation and delay. The delay spread
is a parameter commonly used to quantify multipath effects. Multipath leads
to variations in the received signal strength over frequency
and antenna location.

Rate of fading

Time variation of the channel occur if the communicating device (antenna)
and components of its environment are in motion. Closely related to Doppler
shifting, time variation in conjunction with multipath transmission
leads to variation of the instantaneous received signal strength about
the mean power level as the receiver moves over distances on the order
of less than a single carrier wavelength. Time variation of the channel
becomes uncorrelated every half carrier wavelength
over distance.

Fortunately, the degree of time variation within an indoor system is
much less than that of an outdoor mobile system. One manifestation of time
variation is as spreading in the frequency domain (Doppler
spreading). Given the conditions of typical indoor wireless systems,
frequency spreading should be virtually nonexistent. Doppler spreads of
0.1 - 6.1 Hz (with RMS of 0.3 Hz) have been reported.

Some researchers have considered the effects of moving people. In particular
it was found by Ganesh and Pahlavan [9] that a line of sight delay spread
of 40 ns can have a standard deviation of 9.2 - 12.8 ns. Likewise an obstructed
delay spread can have a std. dev. of 3.7 - 5.7 ns.

For wireless LANs this could mean that an antenna place in a local multipath
null, remains in fade for a very long time. Measures such as diversity
are needed to guarantee reliable communication irrespective of the position
of the antenna. Wideband transmission, e.g. direct sequence CDMA, could
provide frequency diversity.

Indoor RF propagation at 2.4 GHz in Cory Hall at UC Berkeley.

For the infopad project at the University of California, Berkeley
propagation measurements have been conducted in Cory Hall, the home of
the EECS department.

The measured rms delay spreads ranged from 16 - 52 ns. Delay spread
increased with transmitter/receiver distance as well as room dimensions.
The delay spread in the hallway was relatively constant when compared to
the other rooms. The path loss drop off rates were 1.72 in the hallway,
1.99 in room 307 and 2.18 in room 550. Significant signal transmission
occurs through the walls. For the U.C. Berkeley Cory Hall building, this
suggests that walls can not be used as natural cell boundaries.

Indoor Measurement Environment

We made measurements in three rooms and one hallway of Cory Hall as
follows:

In all of the tests, the channel was kept stationary while the transfer
function H'(f) was measured in the sense that no non-essential movement
occurred during a single sweep of frequencies except that required to operate
the test equipment. To average out fading, the receive and transmit antennas
were slightly varied over position for each given separation distance between
the two antennas. Thus, for each separation distance a set of measurements
were taken where we define a measurement as being the response from a single
sweep over frequency of the network analyzer. During the course of a set
of measurements, the amount of position variation between each individual
measurement was approximately one half of the carrier wavelength. This
ensured that the various measurements of the set would be uncorrelated.

Delay Spread

Essentially we treat the instantaneous impulse response as a pdf of
various values of excess delay where excess delay is defined as all possible
values of delay in the instantaneous impulse response after subtracting
off the delay of the fastest arriving signal component. We then numerically
calculate the mean excess delay and the rms delay spread of this pdf. In
determining delay spread, we calculate a power level as the area under
the instantaneous impulse response curve.

The first point to note is that the rms value generally increases with
distance. Heuristically this can be explained by the idea that with greater
distance, the long distanced reflections are relatively stronger (compared
to the line-of-sight) to their contribution to an increased delay spread
is more significant.

Note further that the smallest delay spreads are found in the hallway.
The width of the hallway was less than 8 feet as compared to over 12 feet
for Room 400 well above 20 feet for the other two rooms. These small dimensions
in conjunction with the relative absence of obstacles resulted in a delay
spread that was essentially independent of distance. Heuristically we can
say that increasing the distance did not result in a greater number of
multipath reflections. Consistent with the above is the fact that delay
spread is directly proportional to the general dimensions of the rooms
within which measurements were taken. Thus, Room 550 produced the greatest
delay spreads and likewise Room 550 was the largest room.

FIGURE: RMS Delay Spread vs. Antenna Separation Distance

The Figures below exhibit instantaneous impulse responses from measurements
in Room 550. These two figures serve as examples of different respective
arrival times for the first and the strongest received signal component
arrival times. Measurements have been taken at a 35 foot received-transmit
separation distance.

FIGURE: Impulse Response

FIGURE: Impulse Response

Path Loss

As the three graphs show, signal strength drops off faster as dimensions
of the room increase. In the case of the hallway, the drop off rate was
significantly smaller than 2.0 which is the value for free space loss.
The explanation for this is that the hallway acts as a waveguide given
its small width. Note that the received power levels in these Figures are
in dB (not in dBm) and are with respect to +10 dBm. To obtain absolute
power values in the figure, 10 dB must be added to each component. Note
further that n is based on log-log data although the graphs shown
are log-linear.

Each K-factor is the result from an average of eight measurements taken
from the same transmitter/receiver separation distance. Note that the K-factors
are independent of distance and the three results shown are very close
to one another. In all cases the presence of a line of sight path was the
same. Given that the above measurements all had a LOS path available, one
would expect that the ratio of the strongest received signal component
to the reflected components would be the same. Our measurements bear this
out.

Discussion for Wideband CDMA System

Delay Spread and Resolvable Paths

One of the advantages of direct sequencing spread spectrum is the ability
to distinguish between differing signal path arrivals. These resolvable
paths can then be used to mitigate corruption caused by the channel. Delay
spread is directly related to the number of resolvable paths. The rms delay
spread in Cory Hall ranged from 16 to 52 ns. Given the proposed InfoPad
downlink CDMA chip rate of several tens of Megachips per second, we arrive
at the following:

2 - 3 Resolvable Paths Room 307

3 - 4 Resolvable Paths Room 550

2 - 3 Resolvable Paths Room 400

2 Resolvable Paths Hallway

For CDMA systems with smaller chip rates the channel would behave as
a narrowband, i.e., frequency nonselective channel.

Path Loss, Wall Penetration and Cell Layout

An important issue for indoor cellular reuse systems is the possibility
of interference from users in adjacent cells. In designing cells it would
be convenient if natural barriers such as walls and ceilings/floors could
be used as cell boundaries. With these thoughts in mind, we took measurements
through walls of Cory Hall.

The instantaneous impulse response was taken on the 5th floor of Cory
Hall. The transmitter was located in room 550 and the receiver was located
in the corridor near the freight elevator. The received powers shown are
with respect to +10 dBm so that absolute values can be obtained by adding
10 to magnitudes shown. Clearly the received signal strength through the
wall is significant and shows that some of the walls in Cory Hall can not
serve as cell boundaries. Note that certain walls in Cory consist of different
materials than those on the 5th floor. Most notably room 473 was once an
anechoic chamber and is essentially a metal cage. With these exceptions,
we reiterate that most walls in Cory can not serve as cell boundaries.

An antennaradiation pattern or antenna pattern is
defined as "a mathematical function or graphical representation of
the radiation properties of the antenna as a function of space coordinates.
In most cases, the radiation pattern is determined in the far-field region
(i.e.in the region where electric and magnetic fields vary inversely
with distance) and is represented as a function of the directional coordinates."
The radiation property of most concern is the two- or three-dimensional
spatial distribution of radiated energy as a function of an observer's
position along a path or surface of constant distance from the antenna.
A trace of the received power at a constant distance is called a power
pattern. A graph of the spatial variation of the electric or magnetic
field along a contant distance path, is called a field pattern.

An isotropic antenna is defined as "a hypothetical
lossless antenna having equal radiation in all directions." Clearly,
an isotropic antenna is a ficticious entity, since even the simplest antenna
has some degree of directivity. Although hypothetical and not physically
realizable, an isotropic radiator is taken as a reference for expressing
the directional properties of actual antennas. A directional antenna
is one "having the property of radiating or receiving electromagetic
waves more effectively in some directions than in others." The term
is usually applied to an antenna whose maximum directivity is significantly
greater than that of a linear dipole antenna. The power pattern of a half-wave
linear dipole is shown below.

The linear dipole is an example of an omnidirectional antenna
-- i.e. an antenna having a radiation pattern which is nondirectional
in a plane. As the figure above indicates, a linear dipole has uniform
power flow in any plane perpendicular to the axis of the dipole and the
maximum power flow is in the equatorial plane. One important class of directional
antennas are form from linear arrays of linear dipoles as illustrated below.
The most famous and ubiquitous member of this class is the so called Uda-Yagi
antenna shown on the right.

As example of array patterns, the highly directional power pattern of
an end-fire linear array of 8 half-wave linear dipoles is shown
below.

Like the Uda-Yagi antenna, the end-fire array picture here has is its
maximum maximum power flow in a direction parallel to the line along which
the dipoles are deployed. The power flow in the opposite or back direction
is negligible!

Antenna Terms:

Directivity: The directivity of a transmitting antenna is defined
as the ratio of the radiation intensity flowing in a given direction to
the radiation intensity averaged over all direction. The average radiation
intensity is equal to the total power radiated by the antenna divided by
4. If the direction
is not specified, the direction of maximum radiation intensity is usually
implied. Directivity is some times refered to as directive gain.

Absolute gain: The absolute gain of a transmitting antenna in
a given direction is defined as the ratio of the radiation intensity flowing
in that direction to the radiation intensity that would be obtained if
the power accepted by the antenna were radiated isotropically. If
the direction is not specified, the direction of maximum radiation intensity
is usually implied. (Absolute gain is closely related to directivity, but
it takes into account the efficiency of antenna as well as its direction
characteristics. To distinquish it, the absolute gain is some times refered
to as power gain.)

Relative gain: The relative gain of a transmitting antenna in
a given direction is defined as the ratio of the absolute gain of the antenna
in the given direction to the absolute gain of a reference antenna in the
same direction. The power input to the two antennas must be the same.

Efficiency: The efficiency of a transmitting antenna is the
ratio of the total radiated power radiated by the antenna to the input
power to the antenna.

Effective area (aperature): The effective area or aperature
of a receiving antenna in a given direction is defined as the ratio of
the available power at the terminals of the antenna to the radiation intensity
of a plane wave incident on the antenna in the given direction. If the
direction is not specified, the direction of maximum radiation intensity
is usually implied. It can be shown, that when an isotropic area is used
as a receiving antenna its effective area is the wavelength squared divided
by 4. Thus, the gain of a receiving
antenna is the ratio of the antennas effective area to that of an isotropic
antenna -- i.e..

Antenna factor: The ratio of the magnitude of the electric field
incident upon a receiving antenna to the voltage developed at the antenna's
output connector (assuming a 50 ohm coxial connector) is called the antenna
factor. The antenna factor is clearly related to the gain of antenna, but
is often found to be the most convenience parameter for use in the monitoring
of electromagnetic emissions.

Some of this material was taken from Antenna
Theory: Analysis and Design (2nd edition), Constantine A. Balanis,
John Wiley and Sons, Inc. (1997)